Displaying similar documents to “On Bochner-Martinelli residue currents and their annihilator ideals”

On the Briançon-Skoda theorem on a singular variety

Mats Andersson, Håkan Samuelsson, Jacob Sznajdman (2010)

Annales de l’institut Fourier

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Let Z be a germ of a reduced analytic space of pure dimension. We provide an analytic proof of the uniform Briançon-Skoda theorem for the local ring 𝒪 Z ; a result which was previously proved by Huneke by algebraic methods. For ideals with few generators we also get much sharper results.

The Nash problem of arcs and the rational double points D n

Camille Plénat (2008)

Annales de l’institut Fourier

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This paper deals with the Nash problem, which consists in comparing the number of families of arcs on a singular germ of surface U with the number of essential components of the exceptional divisor in the minimal resolution of this singularity. We prove their equality in the case of the rational double points D n ( n ≥ 4 ).

On Halphen’s Theorem and some generalizations

Alcides Lins Neto (2006)

Annales de l’institut Fourier

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Let M n be a germ at 0 ∈ ℂ m of an irreducible analytic set of dimension n , where n ≥ 2 and 0 is a singular point of M . We study the question: when does there exist a germ of holomorphic map φ : ( ℂ n , 0 ) → ( M , 0 ) such that φ - 1 ( 0 ) = { 0 } ? We prove essentialy three results. In Theorem 1 we consider the case where M is a quasi-homogeneous complete intersection of k polynomials F = ( F 1 , ... , F k ) , that is there exists a linear holomorphic vector field X on ℂ m , with eigenvalues λ 1 , ... , λ m ∈ ℚ + such that X ( F T ) = U · F T , where U is a k × k matrix with entries in 𝒪 m . We prove that if...

Valuations and asymptotic invariants for sequences of ideals

Mattias Jonsson, Mircea Mustaţă (2012)

Annales de l’institut Fourier

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We study asymptotic jumping numbers for graded sequences of ideals, and show that every such invariant is computed by a suitable real valuation of the function field. We conjecture that every valuation that computes an asymptotic jumping number is necessarily quasi-monomial. This conjecture holds in dimension two. In general, we reduce it to the case of affine space and to graded sequences of valuation ideals. Along the way, we study the structure of a suitable valuation space. ...

Computing limit linear series with infinitesimal methods

Laurent Evain (2007)

Annales de l’institut Fourier

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Alexander and Hirschowitz determined the Hilbert function of a generic union of fat points in a projective space when the number of fat points is much bigger than the greatest multiplicity of the fat points. Their method is based on a lemma which determines the limit of a linear system depending on fat points approaching a divisor. Other Hilbert functions were computed previously by Nagata. In connection with his counter-example to Hilbert’s fourteenth problem, Nagata determined...